Results 11 to 20 of about 177 (119)
Valuations on Structures More General Than Fields [PDF]
Computer Sciences & Mathematics Forum, 2023 Valuation theory is an important area of investigation in algebra, with applications in algebraic geometry and number theory. In 1957, M. Krasner introduced hyperfields, which are field-like objects with a multivalued addition, to describe some ...
Alessandro Linzi
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Generalized Centroid of Hyperrings [PDF]
Discussiones Mathematicae - General Algebra and Applications, 2022 In this paper, the notion of generalized centroid is applied to hyperrings. We show that the generalized centroid C of a semiprime hyperring R is a regular hyperring. Also, we show that if C is a hyperfield, then R is a prime hyperring.
Yazarli Hasret +2 more
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Commutative hypergroups associated with a hyperfield [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2017 Let [Formula: see text] be a commutative hypergroup and [Formula: see text] a discrete commutative hypergroup. In this paper we introduce a commutative hypergroup [Formula: see text] associated with a hyperfield [Formula: see text] of [Formula: see text] based on [Formula: see text].
Heyer, Herbert +3 more
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Screened Poisson Hyperfields for Shape Coding [PDF]
SIAM Journal on Imaging Sciences, 2014 Summary: We present a novel perspective on shape characterization using the screened Poisson equation. We discuss that the effect of the screening parameter is a change of measure of the underlying metric space. Screening also indicates a conditioned random walker biased by the choice of measure.
Riza Alp Güler +2 more
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Perfect matroids over hyperfields [PDF]
arXiv, 2019 19 ...
Bowler, Nathan, Pendavingh, Rudi A.
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Regular Parameter Elements and Regular Local Hyperrings [PDF]
Mathematics, 2021 Inspired by the concept of regular local rings in classical algebra, in this article we initiate the study of the regular parameter elements in a commutative local Noetherian hyperring.
Hashem Bordbar, Irina Cristea
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On the borderline of fields and hyperfields, part Ⅱ – Enumeration and classification of the hyperfields of order 7 [PDF]
AIMS Mathematics127 pages, 305 tables Subj-class: math.RA - Rings and Algebras MSC-class: 16Y20 (Primary); 20N20 (Secondary) We extend the results of our previous papers and we reduce the axioms of the definition of the hyperfield. This facilitates the construction, enumeration and classification of all the hyperfields of order 7, while also revealing an important ...
Massouros, Christos G. +1 more
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Geometry of tropical extensions of hyperfields [PDF]
Proceedings of the Royal Society of Edinburgh: Section A MathematicsWe study the geometry of tropical extensions of hyperfields, including the ordinary, signed, and complex tropical hyperfields. We introduce the framework of ‘enriched valuations’ as hyperfield homomorphisms to tropical extensions and show that a notable family of them are relatively algebraically closed.
James Maxwell, Ben Smith
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Hypernorm on hypervector spaces over a hyperfield
Journal of AnalysisAbstractHypernorm is a generalization of the notion of a norm on a vector space over a field. In this paper, we consider a hypervector space $$(\mathbb {V}, +)$$ ( V , + ) over a hyperfield, where $$+
Harikrishnan P K, Syam Prasad Kuncham
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Generalising Kapranov's Theorem For Tropical Geometry Over Hyperfields [PDF]
, 2022 Kapranov's theorem is a foundational result in tropical geometry. It states that the set of tropicalisations of points on a hypersurface coincides precisely with the tropical variety of the tropicalisation of the defining polynomial.
James Maxwell, Maxwell, James
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